Mathematical Digest

Short Summaries of Articles about Mathematics in the Popular Press

"All creatures great and small," by John Whitfield. Nature, 27 September 2001, pages 342-344.

A simple mathematical rule governs the relationship between an animal's body mass and the metabolic rate: The metabolic rate is proportional to the mass raised to the power 3/4. This scaling law, which seems to hold universally across all species, was first proposed in the 1930s. But scientists have never understood the reasons why this law should hold. This article describes work by two ecologists and a physicist who have used ideas from fractal geometry to try to understand the 3/4 scaling law. Their theory ``starts with the assumption that evolution has made biological resource-distribution networks maximize the area across which they can take up and release resources and minimize the time and energy needed to transport those resources through the organism,'' the article states. Such networks can be represented mathematically by fractal models. The article discusses some striking results of the new theory as well as the objections of those who believe the theory may be flawed.